Octavian: This says "Go to Alaska. Find Thanatos and free him. Come back by sundown on June twenty-fourth or die."
Mars: Yes. Is that not clear?
Octavian: Well, my lord... usually prophecies are unclear. They're wrapped in riddles. They rhyme, and...
Mars (casually pulling out a grenade): Yes?
Octavian: The prophecy is clear! A quest!
Mars: Good answer.
In Titan's Curse, Percy & Co. track down Nereus, the old man of the sea, so they can shake him up for some answers. When they pass by him in Son of Neptune, Nereus points one bony finger at Percy and mouths, "Don't even think about it."
Frank bashing Alcyoneus repeatedly on the nose with his shield to keep him unconscious while they drag him out of Alaska.
The video-scroll message that is almost at the ending of "Son Of Neptune" can count as funny.
Leo: What's my title? Am I like admiral, or captain, or...
Piper: Repair Boy.
Leo: Very funny, Piper.
This exchange in The Son of Neptune when Hazel and Frank explain the war games to Percy:
Hazel: "No one dies. Well, not usually And if they do-"
Frank:(imitating Vitellius) "They're wimps! Back in my day, we died all the time, and we liked it!"
And this one, between Frank and Percy:
Frank: Can your sword do grenade form?
Percy: No. Shut up.
"Spears are good for subtraction."
Percy is mad because Poseidon gave the Zhangs the power to change shape while he can't, rendering Frank nearly speechless given the terrifyingly awesome powers Percy has revealed; giant fists of Tiber water, exploding water cannon, mini-hurricanes...
Percy's reaction to accidentally finding Polybotes leading the invasion army south toward New Rome.
While it's funny out-of-context, it's even better in context. Spoilers for Mark Of Athena ahead: Percy manages to improvise a plan to scare Chrysaor and his dolphin-men soldiers off the Argo II. This plan involves convincing the dolphin-men that Dionysus is the captain of this boat, since he's the god that turned them into dolphin-men in the first place. Piper and Hazel fake having suddenly gone insane, and Percy hints to Frank that he should pretend to go crazy too, while transforming into a dolphin to really convince them. Unfortunately, Frank doesn't quite catch on to the plan immediately.
Percy: Oh no, Frank's turning into a crazy dolphin!
Percy:I said,Oh no, Frank is turning into a crazy dolphin!
"Nasty creatures. Keto must really hate you guys."
"Yes, the MAP IN CHARLESTON," Frank said loudly, giving Percy a wide-eyed look to make sure he hasn't missed the information. He couldn't have been more obvious if he had held up a large sign that read CLUE!!!!!
During the chaos of some very angry Romans due to a possessed Leo calmly firing at New Rome from the Argo II many fauns took advantage of this and ran off with whatever food they could carry.
One trotted by Annabeth with his arms full of tacos and an entire pineapple between his teeth.
All around the Romans, Charleston Harbor erupted like a Las Vegas fountain putting on a show. When the wall of seawater subsided, the three Romans were in the bay, spluttering and frantically trying to stay afloat in their armor. Percy stood on the dock, holding Annabeth’s dagger.
Percy: You dropped this.
Annabeth: I love you!
Just before Percy, Piper and Jason fight the twins, we get this little conversation:
Percy: I'm getting tired of this guy's shirt.
Piper: Combat time?
Jason: I hate Wonder bread.
House of Hades
A meta-example, but Riordan's dedication before the book even starts:
Annabeth and Percy are up against Nyx, the primordial goddess of Night, who is forty-feet tall, made of darkness, and is in a flying chariot pulled by vampire shadow horses. What do they do? Pretend to be disgruntled tourists traveling Tartarus and distract her long enough to jump into her Mansion of Night. All in some of the funniest chapters in the book.
Nyx: You — miserable — tourists! How dare you not whimper and beg for my autograph and a picture for your scrapbook!
As Percy faces off against Akhys and has found out that he can't touch her due to the Death Mist, he hopes she can't touch him in turn. This leads to an unexpected (but hilarious) bit of 1337 lingo:
He imagined the Fates up in Olympus, laughing at his wistful thinking: LOL, NOOB!